Computational Studies of the Electronic Spectra of Transition-Metal-Containing Molecules James T. Muckerman, Zhong Wang, Trevor J. Sears Chemistry Department, Brookhaven National Laboratory, Upton, NY USA and Hua Hou Chemistry Department, Wuhan University, Wuhan, P.R. China 62 nd Ohio State University International Symposium on Molecular Spectroscopy June 18-22, 2007

Outline Lingering issues regarding our previous calculations on FeH and VH Diabolical features of the low-lying electronic states of TiC 2 The electronic ground state of the titanium metcar, Ti 8 C 12 Focus on the questions that make the treatment of these problems difficult 44

X 4X 4 A 4  a 6a 6 b 6b 6 C 4C 4 c 6c 6 E 4E 4 F 4F 4 B 4B 4 D 4D 4 X 5X 5 55 55 55 55 33 33 33 33 Lingering issues regarding our previous calculations on FeH and VH

66 11 77 33 88 44 99 10  11  55

Lingering Issues Regarding our Previous Calculations on FeH and VH Focus on the C 4  state of FeH, the B 5  + state of VH, and dipole moments We believed that our previous results for the C 4  state of FeH (C(0)~0.89) and the B 5  + state of VH (C(0)~0.96) could be improved with a better choice of reference function such as we did for the B 4   and D 4  + states of FeH. It would probably be better not to use the same orbitals for the 4  and 4  states of FeH and the 5  ± and 5  states of VH, but rather to perform separate CASSCF calculations with a large weight assigned to the problematic states, followed by MRCI calculations in which the ground and target state roots are computed but only the target state root is retained. Our T e value for the C 4  state of FeH (3791 cm -1 ) is considerably smaller than other calculated values (4759 to 6416 cm -1 ), but (perhaps fortuitously) close to the experimental value (3175 cm -1 ). [C. Wilson et al., J. Chem. Phys. (2001)] Our calculated vibrational frequencies are in general agreement with available experimental data and most other calculated values except for the C 4  state of FeH for which our value is considerably smaller.

More Lingering Issues Regarding FeH and VH… Our values of the dipole moments of the various FeH states were computed as the expectation value of the dipole operator with the MRCI wavefunction, and tend to be smaller (by 0.7 to 1.0 D) than the available experimental values and most other theoretical values. They do, however, reflect the experimentally observed [T. C. Steimle et al., J. Chem. Phys. (2006)] difference between the values for the X 4  and the F 4  states of FeH that, according to our analysis, arises from the F state originating primarily from the  1  7 configuration of the Fe atom while the X state originates primarily for the  2  6 configuration. The dependence of the computed dipole moments on internuclear distance shows the F state having a smaller magnitude at the equilibrium internuclear distance but a much larger derivative than the X state. These results contrasts with those of Tanaka et al. [K. Tanaka et al., J. Chem. Phys. (2001)] that predict similar values and derivatives of the dipole moments of the F and X states.

Still More Lingering Issues Regarding FeH and VH… With the exception of the B 5  + state, there is remarkably little difference between the relative energetics of the MRCI and MRCI+Q results of VH. The B 5  + state of VH with principal configuration  2  2 is stabilized relative to the X state by eV by the Davidson correction. This does not seem to be an artifact of a small C(0), which hovers around 0.96, but results from a somewhat larger correlation energy (ca compared to ca Hartree) than the other states. We also could not follow the B 5  + state to separations less than 1.65 Å because this second root of 5 A 1 symmetry converges to a higher-lying state. Our calculated C 5   state, the second root of 5 A 2 symmetry with principal configurations  2 and  2, does not behave in this manner.

F 4F 4 A 4  X 4X 4 b 6b 6 c 6c 6 C 4C 4 a 6a 6 D 4D 4 B 4B 4 E 4E 4 F 4F 4 X 4X 4 b 6b 6 c 6c 6 C 4C 4 a 6a 6 D 4D 4 B 4B 4 E 4E 4 Change in FeH C 4  state MRCI energy by state average re-weighting 80% A 4  :10% C 4  :10% E 4  30% A 4  :70% C 4  :0% E 4  C(0)~0.96C(0)~0.89

X 4X 4 A 4  a 6a 6 b 6b 6 C 4C 4 c 6c 6 E 4E 4 F 4F 4 B 4B 4 D 4D 4 X 4X 4 a 6a 6 b 6b 6 C 4C 4 c 6c 6 E 4E 4 F 4F 4 B 4B 4 D 4D 4 Change in FeH C 4  state MRCI+Q energy by state average re-weighting 80% A 4  :10% C 4  :10% E 4  30% A 4  :70% C 4  :0% E 4 

X 5X 5 55 55 55 55 33 33 33 33 X 5X 5 55 55 55 55 33 33 33 33 Change in VH B 5  + state MRCI energy by state average re-weighting 80% X 5  :10% B 5  + :10% C 5   10% X 5  :85% B 5  + :5% C 5   C(0)~0.98 C(0)~0.96

X 5X 5 55 55 55 55 33 33 33 33 X 5X 5 55 55 55 55 33 33 33 33 Change in VH B 5  + state MRCI+Q energy by state average re-weighting 80% X 5  :10% B 5  + :10% C 5   10% X 5  :85% B 5  + :5% C 5  

X 5X 5 A 5A 5 D 5D 5 B 5B 5 a 3a 3 d 3d 3 c 3c 3 b 3b 3 C 5C 5 80% X 5  :10% B 5  + :10% C 5   10% X 5  :85% B 5  + :5% C 5   Change in VH B 5  + state MRCI dipole moment by state average re-weighting

Dipole Moments (in Debye) of VH Quintet States at their Energy Minima Dipole Moments (in Debye) of FeH 4  States at their Energy Minima Dipole Moments by Expectation Value vs. Applied Electric Field Calculations a C. Wilson et al., J. Chem. Phys. (2001)

Diabolical features of the low-lying electronic states of TiC 2

(7a 1 ) 2 (4b 2 ) 2 (8a 1 ) 2 (9a 1 ) 2 (3b 1 ) 2 (10a 1 ) 1 (5b 2 ) 1  2s  *2s  2p  2p  2p Ti(d) Ti(d) Principal Configuration of 3 B 2 State of TiC 2 N 2 -like C 2 2- Two singly-occupied d orbitals of Ti 2+ Which two d orbitals are occupied? {d z 2, d xz, d yz, d x 2 -y 2, d xy } → {d(a 1 ), d(a 1 ), d(b 1 ), d(b 2 ), d(a 2 )} Two possible principal configurations for most triplet states of TiC 2 : 3 B 2 – (a 1,b 2 ) or (b 1,a 2 ) 3 B 1 – (a 1,b 1 ) or (b 2,a 2 ) 3 A 2 – (a 1,a 2 ) or (b 1,b 2 ) 3 A 1 – only (a 1,a 1 ) These are not distinct states

TOTAL ENERGIES: CI vector a1 b1 b2 a2 CI coefficients … Two Lowest 3 B 2 Electronic States from CAS(12,14) Calculation with Initial Orbitals from (a 1,b 2 ) SCF The first excited 3 B 2 state does NOT have the (b 1,a 2 ) principal configuration… It has mostly excited (a 1,b 2 ) configurations… Similarly, the first excited 3 B 2 state from a CAS(12,14) calculation with initial orbitals from a (b 1,a 2 ) principal configuration does not have the (a 1,b 2 ) principal configuration…

B3LYP Triplet TiC 2 Energies at Optimal Geometries Wachters(spd)+Bauschlicher(f),Ti; cc-pVTZ(spd),C There is a group of low-lying triplet states of TiC 2 that differ only by which two d orbitals of Ti are singly occupied… For a given state symmetry with two possible occupations for the principal configuration, only one of the possible occupations describes the actual state… Convergence of the SCF orbitals is complicated by local minima and depends on the initial orbital occupation, the molecular geometry and the initial guess…

The previous study didn’t quite get it right.. They apparently locked in on the (b 1,a 2 ) principal configuration of the 3 B 2 state, but they almost got the right answer for the wrong reason.

Principal Configurations, dipole moments (Debye), and charge distribution for different electronic states of TiC 2 at CISD optimized geometries a Calculated as an expectation value at the RMRCI level of theory. b Calcuated at CASSCF(12,14) level with uncontracted Wachters(spd)+Bauschlicher(f) basis set for Ti, and Dunning cc-pVTZ(spd) for C.

TiC 2 Relative Energies (in cm -1 ) at Various Levels of Theory Restrict (0,2) in MRCI

Present MRCI Calculations of TiC 2 Triplet States: Wachters(spd)+f, Ti; cc-pVTZ(spd), C

B3LYP Calculations of the TiC 2 3 B 2 & 3 B 1 Potential Energy Surfaces (C 2v ) The ground 3 B 2 state intersects the first excited 3 B 1 state along a line running approximately from (R,  ) = (1.75, 35) to (2.05, 44)

B3LYP Calculations of the TiC 2 3 B 2 & 3 A 2 Potential Energy Surfaces (C 2v ) The ground 3 B 2 state intersects the excited 3 A 2 state along a line running approximately for (R,  ) = (2.15, 28) to (1.75, 36)

State Symmetry Reps. Double Group Symmetry 3 B 2 C 2v B 2 (A 2 +B 1 +B 2 )  B 2 = B 1 + A 2 + A 1 C s A’ (A’+2A”)  A’ = A’ + A” + A” 3 B 1 C 2v B 1 (A 2 +B 1 +B 2 )  B 1 = B 2 + A 1 + A 2 C s A” (A’+2A”)  A” = A” + A’ + A’ 3 A 2 C 2v A 2 (A 2 +B 1 +B 2 )  A 2 = A 1 + B 2 + B 1 C s A” (A’+2A”)  A” = A” + A’ + A’ Conical Intersections in the Triplet Manifold of TiC 2 The spin-orbit splitting of the ground 3 F state of the Ti atom is cm -1 It seems possible that the ground vibronic state of TiC 2 is delocalized over two or three Born-Oppenheimer potential energy surfaces…

The electronic ground state of the titanium metcar, Ti 8 C 12 Ti (o) Ti (i) Ti (o) DFT and most ab initio single-reference CI methods predict a triplet ground state…

The Last 4 Valence Electrons… Ti 8 C   4a 1 7t 2     4t 1 Key issue in determining the molecular symmetry and ground state  Symmetry preserving quintet states Fill the 4a 1 orbital and consider the +2 ion

Ti 8 C LUMO 4t 1 7t 2 5a 1         Bottom line: 2 electrons go into 4a 1 and 2 go into either the 4t 1 or 7t 2 orbital; Jahn-Teller distortion to a lower symmetry.  Symmetry preserving singlet state  Symmetry breaking triplet states Symmetry breaking singlet states The Last 2 Valence Electrons…

There are two states of interest in each symmetry, mainly different in the HOMO (either on Ti (i) d z 2 or on Ti (o) d xy interacting with C-C  * orbital) HOMO1 (4t 1 ) HOMO2 (7t 2 ) Jahn-Teller Distortion: D 2d & C 3v symmetries a a Energies in kcal/mol relative to the lowest-energy configuration at the same level of theory. Singlet state

CAS(4,10) Comparison of Singlet & Triplet Energies  E(CAS) =  kcal/mol 49a a a (32b 1,32b 2 ) a (31b 1,31b 2 ) a a a 2 HOMO singleta 2 b 2 triplet

Singlet & Triplet MRCI Energies with CAS(4,10) Reference Function  E(MRCI+Q) =  kcal/mol Basis: Ti, Bauschlicher-ANO(spdf); C, 6-31G*(spd) # internal configurations = 225 # contracted configurations = 4,029,687 # internal configurations = 252 # contracted configurations = 3,643,308 a 2 HOMO singleta 2 b 2 triplet

CAS(16,14) 1 A 1 (b2 HOMO) CI vector ========================== a1 b1 b2 a2 coefficient ========================== TOTAL ENERGY a2 homo b2 homo a2b2 triplet ee triplet a2 homo b2 homo a2b2 triplet ee triplet b2 homo a2b2 triplet becomes b2 homo

End The work at Brookhaven National Laboratory was funded under contract DE-AC02-98CH10886 with the U.S. Department of Energy and supported by its Division of Chemical Sciences, Geosciences & Biosciences, Office of Basic Energy Sciences.